This is amazing!! I learnt so much not just about the algorithm, but key concepts like merge sort, masters method and more. I'm waiting for the day you blow up 🔥 def sending this one to my friends
Some feedback about calculating the time complexity you say, the return statement has complexity O(n) but if you observe closely, the whole return statement is filled with O(1) operations, I think the function "ad_plus_bc" has complexity of T(n/2)+O(n), because it has a subtraction operation, subtracting/adding has complexity of O(n) The overall expression of complexity is correct. T(n) = 3T(n/2) + O(n) + O(1), where O(1) can be ignored in the presence of O(n)
Hi, PLEASE create more videos like this and Also add videos to playlist for easy lookup. Really appreciate it. Algo/problems related to Data science would be great as well.
Apart from good explanation. The entire presentation is also so satisfying and I can see u put a lot of work behind it. Do more of them we will keep supporting you sir.
Fantastic and easy to understand tutorial! Just want to point out that the last line of code might not work in the case of an odd number of digits, since you calculate half with n//2.
Thank you for this video. Keep growing. It would be so great if in future you plan on making a course on data structures & algorithms- would probably be something to watch out for whenever computer geeks open youTube.
With quantum computer memories sometime in the future, if read only quantum memories could be invented, then huge indexed table could be used for instantaneous results. For single value function like trig functions, read only index tables would have advantage of single clock speed and absolute accuracy, as it is my understanding that different approximations have needed accuracy for only portions of the number space.
I was wondering from some time ago if Toom-4 is equivalent with Karatsuba , from a complexity point of view, but that looks a bit impossible. Lately , I was able only to come with this. Considerring Toom-4 and also Toom-4 added those two terms multiplications (the ones from middle ), which are more like K-idea, only with two more multiplication comparing too Toom-4. (so we got 4+3 vs 4+5 complexity dilema). those 5 multiplications terms computed are all following some simple rule for product of 2 coetients and other 2, no matter which one of the 5 mult term we chose. So we might be able to reach to the conclusion that we can find the method Florin-4, Florin-8, etc, no so sure about its complexity thow so this may be just some joke offered by me to anyone wish to verify its complexity. Thank You, I like these style of videos on RUclips! ^_^ P.S. digging this out i was needed to reformulate the K-idea , both with Toom one, by switching from geometric progressions to something more oriented on adds n diffs instead coetient products that looks the same to diffs that look the same. But this is a bit too complex to me, a bit hard to get the job done, need meds 2 times a day in any case, I mean only to be able to put these here, for example. Thank You! :-)
@@mehdididit Alrite, here some more nonsense, that might worth some translation 🙂 consider ca in mod normal, logica de tip chat bot sau click programming / logic explorer, pentru utilizatori incepatori din gimnaziu/liceu ar cam trebui sa mearga binisor, ma gandesc ca macar atata pedagogie cibernetica ar cam trebui sa se gaseasca pe lume, spre exemplu la programarea in basic, sa ofere pe post de "mutare" din partea computerului, cateva optiuni pentru urmatoarea nstructiune de inserat , doar cu un click, in viitorul mic cod sursa al rutnei respective, provocarea fiind ca la per total, aplicatia gen logic explorer sa ma arate a ceva. Multumesc frumos!
hey amaizing video but i dont get it why in the time complexity calaculate the sum require o(n) it all sum why not o(1)? i mean at 8:20 at the below statement ?
An algo optimisation idea that can be inspired by the hardware predication techniques, applied to soft data numbers to be multiplied, arraies to be multiplied, others may too, I think that may give us something to think about. Never tested nor verified by me, sorry! :-)
How does this work IN PRACTICE for standard 64 bit binary machines? Is there REALLY a savings? Or are much larger numbers (256 bit) needed for a practical improvement? Has this ever actually been implemented into processor microcode? If so, how did it work out?
The trick is the part at 3:26. Divide and conquer works only if breaking a problem down and dealing with the sum of those smaller chunks is easier. It might not be, you might just end up with many small problems which added up is still the same problem. This is the case if you split two numbers you want to multiply, now you have twice the number of multiplications of integers half the original size. Split again, now 4 times the number of multiplications with integers of a quarter size. Same problem. But here, whenever you split two integers there's 3 new multiplications instead of 4. So you get to split the integers in half without doubling the multiplications needed.
I have a fat expensive algorithm book in my hand that could not even explain how x became a*10^(n/2) + b. Yet it only took you 10 seconds to explain it...
Nice video but i don t understand why do we need this. Cant we just multiply the numbers? Initially i thought that the method will be for that numbers that when are multiplied are giving a very large number that doesn t fit into long long or double.
It's not about overflow because because we could use strings instead anyway, it's about the method we use to actually multiply the numbers. For small numbers we can use the brute force method we all know, but for big numbers, it's better to use the Karatsuba algorithm because it's faster
It is for numbers that have hundreds of digits. Think about numbers like the number of nanoseconds since Jan 1, 1492. Or pi to the 100'th decimal place. On a 32 bit machine, what if you need to multiply two 14-digit numbers.
Discover the new graph theory algorithms course: inscod.com/graphalgo
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/ \
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I believe there's a typo at 6:01 - the fifth line should say "(a+b)(c+d)-ac-bd"
Thanks man
Jeez, you explain this very well. You don’t explain material in a generic way. Also, I love the animation.
Oh thanks a lot!
this is a very well done video, the animation and the color palate are really smooth and the explanation is clear as day. Subscribed.
Thanks a lot for your comment!
This is amazing!! I learnt so much not just about the algorithm, but key concepts like merge sort, masters method and more. I'm waiting for the day you blow up 🔥 def sending this one to my friends
Amazing! Thanks for the comment and the support
Really liked the tree visualtion, made it so much easier to understand.
this is a very well done video, the animation and the color palate are really smooth and the explanation is clear as day.
Some feedback about calculating the time complexity
you say, the return statement has complexity O(n) but if you observe closely, the whole return statement is filled with O(1) operations,
I think the function "ad_plus_bc" has complexity of T(n/2)+O(n), because it has a subtraction operation, subtracting/adding has complexity of O(n)
The overall expression of complexity is correct.
T(n) = 3T(n/2) + O(n) + O(1), where O(1) can be ignored in the presence of O(n)
Best explanation of karatsuba algorithm.
Hi, PLEASE create more videos like this and Also add videos to playlist for easy lookup. Really appreciate it. Algo/problems related to Data science would be great as well.
Thanks for your suggestion!
2 minutes in and i already have a much better understanding. absolute legend thank you!!
Great explanation ! Underrated 100%
Apart from good explanation. The entire presentation is also so satisfying and I can see u put a lot of work behind it. Do more of them we will keep supporting you sir.
Thanks a lot!
This is some high quality material. Really appreciate it.
Thanks a lot!
I never knew that there is another algorithm to multiply. Thanks for increasing my knowledge 😍😍🥰🙏✌️
You're welcome!
One minor thing that is missing here is how to Actually calculate big numbers that don't fit regular programming primitives as Int or Double
We need more such videos
Your channel is getting addictive ❤
Fantastic and easy to understand tutorial! Just want to point out that the last line of code might not work in the case of an odd number of digits, since you calculate half with n//2.
thanks for the video explaination.
also, note that 1.58 is read as one point five eight, not one point fifty eight.
This tip seems very helpful. Thank you for sharing
You're welcome!
Exactly what I was looking for
Thanks !
Thank you so much, been looking for ways to make my multiplication more efficient
Ur explanation is very clear i hope to make more videos about unknown topics in computer science
well done bro .
Thankss
@@insidecode u deserve more .
Great platform and very helpful!! Keep Going! One of the rare channels which explain algorithm design in such depth...
This channel only need playlist clarification and it is perfect!
I'll make playlists then
@@insidecode Thank you!
@@jeffbezos3942 You're welcome!
Thank you for this video. Keep growing. It would be so great if in future you plan on making a course on data structures & algorithms- would probably be something to watch out for whenever computer geeks open youTube.
Thanks for your suggestions
With quantum computer memories sometime in the future, if read only quantum memories could be invented, then huge indexed table could be used for instantaneous results. For single value function like trig functions, read only index tables would have advantage of single clock speed and absolute accuracy, as it is my understanding that different approximations have needed accuracy for only portions of the number space.
amazing explanation,short and brief...made the concept easy for me. thanks 😍
Very well done video. I appreciate the care and quality.
teaching can't be better. thank you.
this video saved my life! thanks
I was wondering from some time ago if Toom-4 is equivalent with Karatsuba , from a complexity point of view, but that looks a bit impossible. Lately , I was able only to come with this. Considerring Toom-4 and also Toom-4 added those two terms multiplications (the ones from middle ), which are more like K-idea, only with two more multiplication comparing too Toom-4. (so we got 4+3 vs 4+5 complexity dilema). those 5 multiplications terms computed are all following some simple rule for product of 2 coetients and other 2, no matter which one of the 5 mult term we chose. So we might be able to reach to the conclusion that we can find the method Florin-4, Florin-8, etc, no so sure about its complexity thow so this may be just some joke offered by me to anyone wish to verify its complexity. Thank You, I like these style of videos on RUclips! ^_^
P.S. digging this out i was needed to reformulate the K-idea , both with Toom one, by switching from geometric progressions to something more oriented on adds n diffs instead coetient products that looks the same to diffs that look the same. But this is a bit too complex to me, a bit hard to get the job done, need meds 2 times a day in any case, I mean only to be able to put these here, for example. Thank You! :-)
Mucho texto
@@mehdididit I agree, I talk too much since I know myself >
@@mehdididit Alrite, here some more nonsense, that might worth some translation 🙂
consider ca in mod normal, logica de tip chat bot sau click programming / logic explorer, pentru utilizatori incepatori din gimnaziu/liceu ar cam trebui sa mearga binisor, ma gandesc ca macar atata pedagogie cibernetica ar cam trebui sa se gaseasca pe lume, spre exemplu la programarea in basic, sa ofere pe post de "mutare" din partea computerului, cateva optiuni pentru urmatoarea nstructiune de inserat , doar cu un click, in viitorul mic cod sursa al rutnei respective, provocarea fiind ca la per total, aplicatia gen logic explorer sa ma arate a ceva.
Multumesc frumos!
thank you!! best explanation of the concept imo
Fantastic as usual! May I ask what program you use to do your videos?
Thanks! I make the slides with PowerPoint
Hahahahaha i was expecting some rare program, thats amazon amazon slides bro. Keep it simple
Just wow! Thanks man... Keep up the good work!
You're welcome!
Brilliant explaination
Never knew about this,might come in handy
Thanks :)
You're welcome!
Brilliant video. Thank you so much
It should be (a+b)(c+d) and you solved for that only but you have written (a+c)(b+d) at 6:10
Yup that's true thanks for mentioning it
Amazingly clear
Amazing explanation
great explanation thanks alot for saving the day
Great explanation, Thank you
thank you this is so useful ,god bless you
This begs to be a homework problem in recursive LISP. Using binary numbers. LOL
amazing explaination bro!
Thank you this is so helpful :)
Subscribed Sir,Amazing work
His speech melody tells 'it's all very simple, seeee?' - My brain sounds drop to 40hz.
hey amaizing video but i dont get it why in the time complexity calaculate the sum require o(n)
it all sum why not o(1)?
i mean at 8:20 at the below statement ?
Did not understand why there's O(n) ? All the operations are O(1)
Additions
An algo optimisation idea that can be inspired by the hardware predication techniques, applied to soft data numbers to be multiplied, arraies to be multiplied, others may too, I think that may give us something to think about. Never tested nor verified by me, sorry! :-)
wow this helped so much thanks youuuu!!!!
You're welcome!
I can't understand why we store n // 2 in the variable half , I know it gives a wrong answer if we don't do that but why ?
Technically you don't need to do it, you can write n//2 everywhere but using a variable gives a more understandable code
How does this work IN PRACTICE for standard 64 bit binary machines? Is there REALLY a savings? Or are much larger numbers (256 bit) needed for a practical improvement?
Has this ever actually been implemented into processor microcode? If so, how did it work out?
According to Wikipedia, at least 320-640 bits.
That algorithm is used to multiply big Matrix right?
just integers, maybe you're talking about Chain matrix multiplication?
@@insidecode yes, looks like it can be applied on that case too
Nice man 👍 keep up the good work
Thanks!
Pardon me but i m still confused how does exactly it reduces the time complexity than the old way, i see a lot of arithmetic in this method too?
The trick is the part at 3:26. Divide and conquer works only if breaking a problem down and dealing with the sum of those smaller chunks is easier. It might not be, you might just end up with many small problems which added up is still the same problem. This is the case if you split two numbers you want to multiply, now you have twice the number of multiplications of integers half the original size. Split again, now 4 times the number of multiplications with integers of a quarter size. Same problem. But here, whenever you split two integers there's 3 new multiplications instead of 4. So you get to split the integers in half without doubling the multiplications needed.
When I was in university I was assigned to implement this algorithm, and I struggled to understand it.
Hi bro, that's realy high quality content
I love ❤❤❤❤❤❤❤your accent daaam.
Keep doing, Love from India🇮🇳🇮🇳.
Thanks a lot man
How to solve it using array by storing two numbers in 1D array with help of 2D array
How do we do this if we have odd lengths of numbers?
I have a fat expensive algorithm book in my hand that could not even explain how x became a*10^(n/2) + b. Yet it only took you 10 seconds to explain it...
very great explanation!
Thanks!
is there another way to get 3 multiplications?
wow , its always worth watching
Thanks!
awesome man immediately subscribe to your channel
Thanks!
PayPal link for paying back for this amazing explanation?
This is helpful .. Thumbs up!
Thanks!
informative, thanks
Nice video but i don t understand why do we need this. Cant we just multiply the numbers? Initially i thought that the method will be for that numbers that when are multiplied are giving a very large number that doesn t fit into long long or double.
It's not about overflow because because we could use strings instead anyway, it's about the method we use to actually multiply the numbers. For small numbers we can use the brute force method we all know, but for big numbers, it's better to use the Karatsuba algorithm because it's faster
It is for numbers that have hundreds of digits. Think about numbers like the number of nanoseconds since Jan 1, 1492. Or pi to the 100'th decimal place. On a 32 bit machine, what if you need to multiply two 14-digit numbers.
Amazing Video!
Thanks!
Thank you!!
Great content. Thank you
You're welcome!
very helpful video, thanks heaps
You're welcome!
Really really useful
thanks!
Why calculating the result takes O(n)?
Addition digit by digit is an O(n) for n digits
سبحان الله والله عرفت accent تعك دزيرية 😂
Anyways, thanks for the information it was really helpful, keep going 💜💜
You're welcome kho
cool ♣
thank u a lot bro .... best video ;)
You're welcome!
The best channel
Hey thanks!
If you talked a bit slower and clearer would be a 10/10
Beautiful!
Thank you!
I don't get it, why n is 2?
Where did you see that n is 2?
Aw this is amazing
beautiful ty
fascinating!
Thank u sir
You're welcome!
Need more such
The next videos will all be about CS algorithms!
Thx a lot
nice job
thanks
that doesn't look quicker or simpler
It's quicker for large numbers, Karatsuba algorithm has an O(n^1.58) time complexity while the brute force method has an O(n²) complexity
Amazing
Calculator was made for the math💀💀
nice man
Thanks for watching!
you are super awesome
Thanks!
goated video
u da goat no bap
thanks a loot